I am really confused by the following question :
A fair six-sided die, equally likely is rolled 5 times, independently. Let X be the number of times that the roll results in 2 or 3. Find the numerical values of the following.
Calculate the pX(2.5) and pX(1)?
My thought process is the following : X being the number of times you have 2 or 3 which means that the probability of having a 2 or a 3 is 1/6 + 1/6 = 1/3
so for pX(1) = 5c1 (1/3)^(1)*(2/3)^(4)
pX(2.5) = I would say, 2.5 times 2 or 3 which means it will pX(0) = 5c0 (1/3)^0(2/3)^5
Do that sounds correct?
Thanks very much
If "pX(k)" stands for $P(X=k)$ then $P(X=2.5)=0$ since $X$ only takes values in $\{0,1,2,3,4,5\}$.
Your reasoning and solution for finding $P(X=1)$ is correct.